Question

Which equation is the inverse of 2(x-2)² = 8(7+ y)?

O-2(x-2)² = -8(7+ y)
Oy-1x²-x-8
O y=-2± √28+4%
Oy=2+√√28+4x

Answer 1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

`2(x-2)^2=8(7+y)\hspace{5em}\stackrel{\textit{quick switcheroo}}{2(y-2)^2=8(7+x)} \\\\\\ (y-2)^2=\cfrac{8(7+x)}{2}\implies (y-2)^2=4(7+x)\implies (y-2)^2=28+4x \\\\\\ y-2=\pm√(28+4x)\implies \boxed{y=2\pm√(28+4x)}\qquad \impliedby f^(-1)(x)`